The figure below shows in dashed lines sinusoidal signals of the same frequency at three different phase shifts. The signals are then sampled such that the sinusoidal frequency is exactly a half of the sampling frequency, i.e. the frequency of all the sinusoids is the Nyquist frequency. The samples taken from this signal are represented by the circles.
From the figure, it seems that the amplitude of the digital sinusoidal signals is dependent upon the sampling rate and instant of sampling. In fact if the sampling times coincide with the zero-crossings of the sinusoid, then no signal will be detected at all.
I had initially thought that sampling a bandlimited analog signal at the appropriate sampling frequency would enable perfect reconstruction, but this counter-example has left me stumped. It seems that this sinusoid will generally not be reconstructed properly if digitized and then reconstructed at this rate. Have I gone wrong in my understanding, and if so, can someone please point me in the right direction?